Electric field calculation

I'm stuck on this question:

Q: The outer conductor (radius b, length l) of a long cylindrical capacitor is earthed. The inner conductor (radius a, length l) is hollow, insulated and uncharged. A sphere of radius R is charged to a potential V far from any other bodies and is inserted inside the inner conductor of the cylindrical capacitor without touching it. (The length l is very much greater than R so end-effects may be ignored). Draw diagrams showing the distributions of the induced charges and the E-field lines in two perpendicular planes through the centre of the sphere, one parallel and one perpendicular to the axis of the cylinder. Show that the electri field strength at a radius a<r<b is E=2RV/rl and hence find the potential of the inner cylinder.

My attempt:

To find the electri field strength E I first tried to find an expression for the charge and integrate it over the limits r and 0, but I'm having problem getting the charge expression. Help would be hugely appreciated.